A hybrid GFDM-DPIM solver for the stochastic response analysis of plate structures

Abstract

In recent years, meshless collocation methods have become an attractive alternative for problems in the field of computational mechanics, but the studies on stochastic response analysis based on these methods are still not enough. In this paper, a novel solver for the stochastic response analysis is proposed by combining the generalized finite difference method (GFDM), a popular meshless collocation method, with the direct probability integral method (DPIM), which is a hybrid GFDM-DPIM solver. This solver uses GFDM to calculate the physical response of the structure and DPIM to obtain the probability density function of the response. Simple form and wide application range are the outstanding advantages of this solver. The effectiveness and accuracy of the proposed solver are validated through three examples involving plate structures, with results compared against those obtained through Monte Carlo Simulation.